TY - GEN
T1 - Finding needles in noisy haystacks
AU - Castro, R. M.
AU - Haupt, J.
AU - Nowak, R.
AU - Raz, G. M.
PY - 2008
Y1 - 2008
N2 - The theory of compressed sensing shows that samples in the form of random projections are optimal for recovering sparse signals in high-dimensional spaces (i.e., finding needles in haystacks), provided the measurements are noiseless. However, noise is almost always present in applications, and compressed sensing suffers from it. The signal to noise ratio per dimension using random projections is very poor, since sensing energy is equally distributed over all dimensions. Consequently, the ability of compressed sensing to locate sparse components degrades significantly as noise increases. It is possible, in principle, to improve performance by "shaping" the projections to focus sensing energy in proper dimensions. The main question addressed here is, can projections be adaptively shaped to achieve this focusing effect? The answer is yes, and we demonstrate a simple, computationally efficient procedure that does so.
AB - The theory of compressed sensing shows that samples in the form of random projections are optimal for recovering sparse signals in high-dimensional spaces (i.e., finding needles in haystacks), provided the measurements are noiseless. However, noise is almost always present in applications, and compressed sensing suffers from it. The signal to noise ratio per dimension using random projections is very poor, since sensing energy is equally distributed over all dimensions. Consequently, the ability of compressed sensing to locate sparse components degrades significantly as noise increases. It is possible, in principle, to improve performance by "shaping" the projections to focus sensing energy in proper dimensions. The main question addressed here is, can projections be adaptively shaped to achieve this focusing effect? The answer is yes, and we demonstrate a simple, computationally efficient procedure that does so.
KW - Adaptive sampling
KW - Compressed sensing
KW - Reconstruction
KW - Sparse approximation
UR - http://www.scopus.com/inward/record.url?scp=51449124089&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=51449124089&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2008.4518814
DO - 10.1109/ICASSP.2008.4518814
M3 - Conference contribution
AN - SCOPUS:51449124089
SN - 1424414849
SN - 9781424414840
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 5133
EP - 5136
BT - 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
T2 - 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
Y2 - 31 March 2008 through 4 April 2008
ER -